arXiv subjects

Ying-Cheng Lai

Publications and source records attributed to Ying-Cheng Lai.

At least 55 records · Page 3Linked to original sources

arXiv2022

Predicting extreme events from data using deep machine learning: when and where

We develop a deep convolutional neural network (DCNN) based framework for model-free prediction of the occurrence of extreme events both in time ("when") and in space ("where") in nonlinear physical systems of spatial dimension two. The measurements or data are a set of two-dimensional snapshots or images. For a desired time horizon of prediction, a proper labeling scheme can be designated to enable successful training of the DCNN and subsequent prediction of extreme events in time. Given that an extreme event has been predicted to occur within the time horizon, a space-based labeling scheme can be applied to predict, within certain resolution, the location at which the event will occur. We use synthetic data from the 2D complex Ginzburg-Landau equation and empirical wind speed data of the North Atlantic ocean to demonstrate and validate our machine-learning based prediction framework. The trade-offs among the prediction horizon, spatial resolution, and accuracy are illustrated, and the detrimental effect of spatially biased occurrence of extreme event on prediction accuracy is discussed. The deep learning framework is viable for predicting extreme events in the real world.

cs.LG↗

arXiv2022

Optical response of two-dimensional Dirac materials with a flat band

Two-dimensional Dirac materials with a flat band have been demonstrated to possess a plethora of unusual electronic properties, but the optical properties of these materials are less studied. Utilizing $α$-$\mathcal{T}_3$ lattice as a prototypical system, where $0\le α\le 1$ is a tunable parameter and a flat band through the conic intersection of two Dirac cones arises for $α> 0$, we investigate the conductivity of flat-band Dirac material systems analytically and numerically. Motivated by the fact that the imaginary part of the optical conductivity can have significant effects on the optical response and is an important factor of consideration for developing $α$-$\mathcal{T}_3$ lattice based optical devices, we are led to derive a complete conductivity formula with both the real and imaginary parts. Scrutinizing the formula, we uncover two phenomena. First, for the value of $α$ in some range, two types of optical transitions coexist: one between the two Dirac cones and another from the flat band to a cone, which generate multi-frequency transverse electrical propagating waves. Second, for $α=1$ so the quasiparticles become pseudospin-1, the flat-to-cone transition can result in resonant scattering. These results pave the way to exploiting $α$-$T_3$ lattice for optical device applications in the terahertz frequency domain.

cond-mat.mes-hall↗

arXiv2022

Continuity scaling: A rigorous framework for detecting and quantifying causality accurately

Data based detection and quantification of causation in complex, nonlinear dynamical systems is of paramount importance to science, engineering and beyond. Inspired by the widely used methodology in recent years, the cross-map-based techniques, we develop a general framework to advance towards a comprehensive understanding of dynamical causal mechanisms, which is consistent with the natural interpretation of causality. In particular, instead of measuring the smoothness of the cross map as conventionally implemented, we define causation through measuring the {\it scaling law} for the continuity of the investigated dynamical system directly. The uncovered scaling law enables accurate, reliable, and efficient detection of causation and assessment of its strength in general complex dynamical systems, outperforming those existing representative methods. The continuity scaling based framework is rigorously established and demonstrated using datasets from model complex systems and the real world.

math.DS↗

arXiv2022

Many-body Hilbert space scarring on a superconducting processor

Quantum many-body scarring (QMBS) -- a recently discovered form of weak ergodicity breaking in strongly-interacting quantum systems -- presents opportunities for mitigating thermalization-induced decoherence in quantum information processsing. However, the existing experimental realizations of QMBS are based on kinetically-constrained systems where an emergent dynamical symmetry "shields" such states from the thermalizing bulk of the spectrum. Here, we experimentally realize a distinct kind of QMBS phenomena by approximately decoupling a part of the many-body Hilbert space in the computational basis. Utilizing a programmable superconducting processor with 30 qubits and tunable couplings, we realize Hilbert space scarring in a non-constrained model in different geometries, including a linear chain as well as a quasi-one-dimensional comb geometry. By performing full quantum state tomography on 4-qubit subsystems, we provide strong evidence for QMBS states by measuring qubit population dynamics, quantum fidelity and entanglement entropy following a quench from initial product states. Our experimental findings broaden the realm of QMBS mechanisms and pave the way to exploiting correlations in QMBS states for applications in quantum information technology.

quant-ph↗

arXiv2021

A Chirality-Based Quantum Leap

Chiral degrees of freedom occur in matter and in electromagnetic fields and constitute an area of research that is experiencing renewed interest driven by recent observations of the chiral-induced spin selectivity (CISS) effect in chiral molecules and engineered nanomaterials. The CISS effect underpins the fact that charge transport through nanoscopic chiral structures favors a particular electronic spin orientation, resulting in large room-temperature spin polarizations. Observations of the CISS effect suggest opportunities for spin control and for the design and fabrication of room-temperature quantum devices from the bottom up, with atomic-scale precision. Any technology that relies on optimal charge transport, including quantum devices for logic, sensing, and storage, may benefit from chiral quantum properties. These properties can be theoretically and experimentally investigated from a quantum information perspective, which is presently lacking. There are uncharted implications for the quantum sciences once chiral couplings can be engineered to control the storage, transduction, and manipulation of quantum information. This forward-looking perspective provides a survey of the experimental and theoretical fundamentals of chiral-influenced quantum effects, and presents a vision for their future roles in enabling room-temperature quantum technologies.

cond-mat.mes-hall↗

arXiv2021

A rigorous and efficient approach to finding and quantifying symmetries in complex networks

Symmetries are fundamental to dynamical processes in complex networks such as cluster synchronization, which have attracted a great deal of current research. Finding symmetric nodes in large complex networks, however, has relied on automorphism groups in algebraic group theory, which are solvable in quasipolynomial time. We articulate a conceptually appealing and computationally extremely efficient approach to finding and characterizing all symmetric nodes by introducing a structural position vector (SPV) for each and every node in the network. We prove mathematically that nodes with the identical SPV are symmetrical to each other. Utilizing six representative complex networks from the real world, we demonstrate that all symmetric nodes can be found in linear time, and the SPVs can not only characterize the similarity of nodes but also quantify the nodal influences in spreading dynamics on the network. Our SPV-based framework, in additional to being rigorously justified, provides a physically intuitive way to uncover, understand and exploit symmetric structures in complex networks.

physics.soc-ph↗

arXiv2021

Tomography of time-dependent quantum spin networks with machine learning

Interacting spin networks are fundamental to quantum computing. Data-based tomography of time-independent spin networks has been achieved, but an open challenge is to ascertain the structures of time-dependent spin networks using time series measurements taken locally from a small subset of the spins. Physically, the dynamical evolution of a spin network under time-dependent driving or perturbation is described by the Heisenberg equation of motion. Motivated by this basic fact, we articulate a physics-enhanced machine learning framework whose core is Heisenberg neural networks. In particular, we develop a deep learning algorithm according to some physics motivated loss function based on the Heisenberg equation, which "forces" the neural network to follow the quantum evolution of the spin variables. We demonstrate that, from local measurements, not only the local Hamiltonian can be recovered but the Hamiltonian reflecting the interacting structure of the whole system can also be faithfully reconstructed. We test our Heisenberg neural machine on spin networks of a variety of structures. In the extreme case where measurements are taken from only one spin, the achieved tomography fidelity values can reach about 90%. The developed machine learning framework is applicable to any time-dependent systems whose quantum dynamical evolution is governed by the Heisenberg equation of motion.

quant-ph↗

arXiv2021

Anticipating synchronization with machine learning

In applications of dynamical systems, situations can arise where it is desired to predict the onset of synchronization as it can lead to characteristic and significant changes in the system performance and behaviors, for better or worse. In experimental and real settings, the system equations are often unknown, raising the need to develop a prediction framework that is model free and fully data driven. We contemplate that this challenging problem can be addressed with machine learning. In particular, exploiting reservoir computing or echo state networks, we devise a "parameter-aware" scheme to train the neural machine using asynchronous time series, i.e., in the parameter regime prior to the onset of synchronization. A properly trained machine will possess the power to predict the synchronization transition in that, with a given amount of parameter drift, whether the system would remain asynchronous or exhibit synchronous dynamics can be accurately anticipated. We demonstrate the machine-learning based framework using representative chaotic models and small network systems that exhibit continuous (second-order) or abrupt (first-order) transitions. A remarkable feature is that, for a network system exhibiting an explosive (first-order) transition and a hysteresis loop in synchronization, the machine learning scheme is capable of accurately predicting these features, including the precise locations of the transition points associated with the forward and backward transition paths.

nlin.AO↗

arXiv2021

Adaptable Hamiltonian neural networks

The rapid growth of research in exploiting machine learning to predict chaotic systems has revived a recent interest in Hamiltonian Neural Networks (HNNs) with physical constraints defined by the Hamilton's equations of motion, which represent a major class of physics-enhanced neural networks. We introduce a class of HNNs capable of adaptable prediction of nonlinear physical systems: by training the neural network based on time series from a small number of bifurcation-parameter values of the target Hamiltonian system, the HNN can predict the dynamical states at other parameter values, where the network has not been exposed to any information about the system at these parameter values. The architecture of the HNN differs from the previous ones in that we incorporate an input parameter channel, rendering the HNN parameter--cognizant. We demonstrate, using paradigmatic Hamiltonian systems, that training the HNN using time series from as few as four parameter values bestows the neural machine with the ability to predict the state of the target system in an entire parameter interval. Utilizing the ensemble maximum Lyapunov exponent and the alignment index as indicators, we show that our parameter-cognizant HNN can successfully predict the route of transition to chaos. Physics-enhanced machine learning is a forefront area of research, and our adaptable HNNs provide an approach to understanding machine learning with broad applications.

cs.LG↗

arXiv2021

Optimal networks for dynamical spreading

The inverse problem of finding the optimal network structure for a specific type of dynamical process stands out as one of the most challenging problems in network science. Focusing on the susceptible-infected-susceptible type of dynamics on annealed networks whose structures are fully characterized by the degree distribution, we develop an analytic framework to solve the inverse problem. We find that, for relatively low or high infection rates, the optimal degree distribution is unique, which consists of no more than two distinct nodal degrees. For intermediate infection rates, the optimal degree distribution is multitudinous and can have a broader support. We also find that, in general, the heterogeneity of the optimal networks decreases with the infection rate. A surprising phenomenon is the existence of a specific value of the infection rate for which any degree distribution would be optimal in generating maximum spreading prevalence. The analytic framework and the findings provide insights into the interplay between network structure and dynamical processes with practical implications.

physics.soc-ph↗

arXiv2020

Quantitative assessment of the effects of resource optimization and ICU admission policy on COVID-19 mortalities

It is evident that increasing the intensive-care-unit (ICU) capacity and giving priority to admitting and treating younger patients will reduce the number of COVID-19 deaths, but a quantitative assessment of these measures has remained inadequate. We develop a comprehensive, non-Markovian state transition model, which is validated through accurate prediction of the daily death toll for two epicenters: Wuhan, China and Lombardy, Italy. The model enables prediction of COVID-19 deaths in various scenarios. For example, if treatment priorities had been given to younger patients, the death toll in Wuhan and Lombardy would have been reduced by 10.4\% and 6.7\%, respectively. The strategy depends on the epidemic scale and is more effective in countries with a younger population structure. Analyses of data from China, South Korea, Italy, and Spain suggest that countries with less per capita ICU medical resources should implement this strategy in the early stage of the pandemic to reduce mortalities.

physics.soc-ph↗

arXiv2020

Finding nonlinear system equations and complex network structures from data: a sparse optimization approach

In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system equations and structure based solely on measured time series. Recently, methods based on sparse optimization have been developed. For example, the principle of exploiting sparse optimization such as compressive sensing to find the equations of nonlinear dynamical systems from data was articulated in 2011 by the Nonlinear Dynamics Group at Arizona State University. This article presents a brief review of the recent progress in this area. The basic idea is to expand the equations governing the dynamical evolution of the system into a power series or a Fourier series of a finite number of terms and then to determine the vector of the expansion coefficients based solely on data through sparse optimization. Examples discussed here include discovering the equations of stationary or nonstationary chaotic systems to enable prediction of dynamical events such as critical transition and system collapse, inferring the full topology of complex networks of dynamical oscillators and social networks hosting evolutionary game dynamics, and identifying partial differential equations for spatiotemporal dynamical systems. Situations where sparse optimization is effective and those in which the method fails are discussed. Comparisons with the traditional method of delay coordinate embedding in nonlinear time series analysis are given and the recent development of model-free, data driven prediction framework based on machine learning is briefly introduced.

math.DS↗

arXiv2020

Machine learning prediction of critical transition and system collapse

To predict a critical transition due to parameter drift without relying on model is an outstanding problem in nonlinear dynamics and applied fields. A closely related problem is to predict whether the system is already in or if the system will be in a transient state preceding its collapse. We develop a model free, machine learning based solution to both problems by exploiting reservoir computing to incorporate a parameter input channel. We demonstrate that, when the machine is trained in the normal functioning regime with a chaotic attractor (i.e., before the critical transition), the transition point can be predicted accurately. Remarkably, for a parameter drift through the critical point, the machine with the input parameter channel is able to predict not only that the system will be in a transient state, but also the average transient time before the final collapse.

cs.LG↗

arXiv2020

Synchronization within synchronization: transients and intermittency in ecological networks

Transients are fundamental to ecological systems with significant implications to management, conservation, and biological control. We uncover a type of transient synchronization behavior in spatial ecological networks whose local dynamics are of the chaotic, predator-prey type. In the parameter regime where there is phase synchronization among all the patches, complete synchronization (i.e., synchronization in both phase and amplitude) can arise in certain pairs of patches as determined by the network symmetry - henceforth the phenomenon of "synchronization within synchronization." Distinct patterns of complete synchronization coexist but, due to intrinsic instability or noise, each pattern is a transient and there is random, intermittent switching among the patterns in the course of time evolution. The probability distribution of the transient time is found to follow an algebraic scaling law with a divergent average transient lifetime. Based on symmetry considerations, we develop a stability analysis to understand these phenomena. The general principle of symmetry can also be exploited to explain previously discovered, counterintuitive synchronization behaviors in ecological networks.

q-bio.PE↗

arXiv2020

Phase diagrams of interacting spreading dynamics in complex networks

Epidemic spreading processes in the real world can interact with each other in a cooperative, competitive, or asymmetric way, requiring a description based on coevolution dynamics. Rich phenomena such as discontinuous outbreak transitions and hystereses can arise, but a full picture of these behaviors in the parameter space is lacking. We develop a theory for interacting spreading dynamics on complex networks through spectral dimension reduction. In particular, we derive from the microscopic quenched mean-field equations a two-dimensional system in terms of the macroscopic variables, which enables a full phase diagram to be determined analytically. The diagram predicts critical phenomena that were known previously but only numerically, such as the interplay between discontinuous transition and hysteresis as well as the emergence and role of tricritical points.

physics.soc-ph↗

arXiv2020

Non-Markovian recovery makes complex networks more resilient against large-scale failures

Non-Markovian spontaneous recovery processes with a time delay (memory) are ubiquitous in the real world. How does the non-Markovian characteristic affect failure propagation in complex networks? We consider failures due to internal causes at the nodal level and external failures due to an adverse environment, and develop a pair approximation analysis taking into account the two-node correlation. In general, a high failure stationary state can arise, corresponding to large-scale failures that can significantly compromise the functioning of the network. We uncover a striking phenomenon: memory associated with nodal recovery can counter-intuitively make the network more resilient against large-scale failures. In natural systems, the intrinsic non-Markovian characteristic of nodal recovery may thus be one reason for their resilience. In engineering design, incorporating certain non-Markovian features into the network may be beneficial to equipping it with a strong resilient capability to resist catastrophic failures.

physics.soc-ph↗

arXiv2020

Anomalous in-gap edge states in two-dimensional pseudospin-1 Dirac insulators

Quantum materials that host a flat band, such as pseudospin-1 lattices and magic-angle twisted bilayer graphene, can exhibit drastically new physical phenomena including unconventional superconductivity, orbital ferromagnetism, and Chern insulating behaviors. We report a surprising class of electronic in-gap edge states in pseudospin-1 materials without the conventional need of band-inversion topological phase transitions or introducing magnetism via an external magnetic type of interactions. In particular, we find that, in two-dimensional gapped (insulating) Dirac systems of massive spin-1 quasiparticles, in-gap edge modes can emerge through only an {\em electrostatic potential} applied to a finite domain. Associated with these unconventional edge modes are spontaneous formation of pronounced domain-wall spin textures, which exhibit the feature of out-of-plane spin-angular momentum locking on both sides of the domain boundary and are quite robust against boundary deformations and impurities despite a lack of an explicit topological origin. The in-gap modes are formally three-component evanescent wave solutions, akin to the Jackiw-Rebbi type of bound states. Such modes belong to a distinct class due to the following physical reasons: three-component spinor wave function, unusual boundary conditions, and a shifted flat band induced by the external scalar potential. Not only is the finding of fundamental importance, but it also paves the way for generating highly controllable in-gap edge states with emergent spin textures using the traditional semiconductor gate technology. Results are validated using analytic calculations of a continuum Dirac-Weyl model and tight-binding simulations of realistic materials through characterizations of local density of state spectra and resonant tunneling conductance.

cond-mat.mes-hall↗

arXiv2020

Scaling law of transient lifetime of chimera states under dimension-augmenting perturbations

Chimera states arising in the classic Kuramoto system of two-dimensional phase coupled oscillators are transient but they are "long" transients in the sense that the average transient lifetime grows exponentially with the system size. For reasonably large systems, e.g., those consisting of a few hundreds oscillators, it is infeasible to numerically calculate or experimentally measure the average lifetime, so the chimera states are practically permanent. We find that small perturbations in the third dimension, which make system "slightly" three-dimensional, will reduce dramatically the transient lifetime. In particular, under such a perturbation, the practically infinite average transient lifetime will become extremely short, because it scales with the magnitude of the perturbation only logarithmically. Physically, this means that a reduction in the perturbation strength over many orders of magnitude, insofar as it is not zero, would result in only an incremental increase in the lifetime. The uncovered type of fragility of chimera states raises concerns about their observability in physical systems.

nlin.AO↗